Sometimes when solving problems involving trigonometry,
we have to use the angle of elevation, which is the angle measured from the horizontal
through which an observer would have to elevate his or her line of sight in order to see
the object.

The angle of depression is the angle measured from the
horizontal, through which an observer has to lower his or her line of sight in order to
see an object.

Examples:

1.

A person is standing 50m from the
base of a tower. The angle of elevation to the top of the tower is 76 degrees. How high
is the tower?

Solution - The Height
of the tower is x. So we have:

tan 76°

=

x / 50

50 tan 76°

=

x

50 (4.0107809)

=

x

200.5m

x

2.

Two people are in a hot air
balloon. One of them is able to get a sighting as it passes over one end of a
football field. The angle of depression to the other end of the football field is
53.8 degrees. This person knows that the length of the football field, including the end
zones is 120 yards. How high was the balloon when it went over the football field?